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Item response theory models in the measurement theory with the use of LTM package in R

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Brzezińska J.
Econometrics. Ekonometria. Advances in Applied Data Analytics
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2018
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issue vol. 22 no. 1
11-25
EN
Item Response Theory (IRT) is an extension of the Classical Test Theory (CCT) and focuses on how specific test items function in assessing a construct. They are widely known in psychology, medicine, and marketing, as well as in social sciences. An item response model specifies a relationship between the observable examinee test performance and the unobservable traits or abilities assumed to underlie performance on the test. Within the broad framework of item response theory, many models can be operationalized because of the large number of choices available for the mathematical form of the item characteristic curves. In this paper we introduce several types of IRT models such as: the Rasch, and the Birnbaum model. We present the main assumptions for IRT analysis, estimation method, properties, and model selection methods. In this paper we present the application of IRT analysis for binary data with the use of the ltm package in R.
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A polytomous item response theory models using R

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Brzezińska J.
Econometrics. Ekonometria. Advances in Applied Data Analytics
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2016
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issue 2 (52)
43-52
EN
Item response theory (IRT) is widely used in educational and psychological research to model how participants respond to test items in isolation and in bundles. Item response theory has replaced classical measurement theory as a framework for test development, scale constructions, scree reporting and test evaluation. The most popular of the item response models for multiple choice tests are the one-parameter (i. e. the Rasch model) and threeparameter models. This is the general framework for specifying the functional relationship between a respondent’s underlying latent trait level, commonly known as ability in educational testing, or the factor score in the factor analysis tradition and an item level stimulus. In this paper, arguments are offered for continuing research and applying multidimensional IRT models. The position is also taken that multi-parameter IRT models have potentially important roles to play in the advancement of measurement theory about which models to use should depend on model fit to the test data. All calculations are conducted in R available from CRAN which is a widely-used and well-known environment for statistical computing and graphics.
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